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Recent work has shown that probabilistic models based on pairwiseinteractions-in the simplest case, the Ising model-provide surprisinglyaccurate descriptions of experiments on real biological networks ranging fromneurons to genes. Finding these models requires us to solve an inverse problem:given experimentally measured expectation values, what are the parameters ofthe underlying Hamiltonian? This problem sits at the intersection ofstatistical physics and machine learning, and we suggest that more efficientsolutions are possible by merging ideas from the two fields. We use acombination of recent coordinate descent algorithms with an adaptation of thehistogram Monte Carlo method, and implement these techniques to take advantageof the sparseness found in data on real neurons. The resulting algorithm learnsthe parameters of an Ising model describing a network of forty neurons within afew minutes. This opens the possibility of analyzing much larger data sets nowemerging, and thus testing hypotheses about the collective behaviors of thesenetworks.

Faster solutions of the inverse pairwise Ising problem